### Clarifications

**Algebra 1 - Fluency Recommendations**

Fluency in adding, subtracting, and multiplying polynomials supports students throughout their work in algebra, as well as in their symbolic work with functions. Manipulation can be more mindful when it is fluent.

**Subject Area:**Mathematics

**Grade:**912

**Domain-Subdomain:**Algebra: Arithmetic with Polynomials & Rational Expressions

**Cluster:**Level 1: Recall

**Cluster:**Perform arithmetic operations on polynomials. (Algebra 1 - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved

**Assessed:**Yes

**Assessment Limits :**

Items set in a real-world context should not result in a nonreal answer if the polynomial is used to solve for the unknown.In items that require addition and subtraction, polynomials are limited to monomials, binomials, and trinomials. The simplified polynomial should contain no more than six terms.

Items requiring multiplication of polynomials are limited to a product of: two monomials, a monomial and a binomial, a monomial and a trinomial, two binomials, and a binomial and a trinomial.

**Calculator :**Neutral

**Clarification :**

Students will relate the addition, subtraction, and multiplication of integers to the addition, subtraction, and multiplication of polynomials with integral coefficients through application of the distributive property.Students will apply their understanding of closure to adding, subtracting, and multiplying polynomials with integral coefficients.

Students will add, subtract, and multiply polynomials with integral coefficients.

**Stimulus Attributes :**

Items may be set in a mathematical or real-world context.Items may use function notation.

**Response Attributes :**

Items may require the student to write the answer in standard form. Items may require the student to recognize equivalent expressions.Items may require the student to rewrite expressions with negative exponents, but items must not require the student to rewrite rational expression as seen in the standard MAFS.912.A-APR.4.7.

**Test Item #:**Sample Item 1**Question:**Roxanne wants to test the idea that polynomials are closed under addition. Her work and explanation are shown.

Drag an expression and phrases to the boxes to complete the statement.

Add to ____________________. The sum is closed because ______________ are ________________ and by definition the sum is a polynomial.

**Difficulty:**N/A**Type:**GRID: Graphic Response Item Display

## Related Courses

## Related Access Points

## Related Resources

## Assessments

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Student Center Activity

## Tutorials

## Unit/Lesson Sequence

## Virtual Manipulatives

## MFAS Formative Assessments

Students are asked to find the sum of two polynomials and explain if the sum of polynomials always results in a polynomial.

Students are asked to multiply polynomials and explain if the product of polynomials always results in a polynomial.

Students are asked to multiply polynomials and explain if the product of two polynomials always results in a polynomial.

Students are asked to find the difference of two polynomials and explain if the difference of polynomials will always result in a polynomial.

## Original Student Tutorials Mathematics - Grades 9-12

Learn how to identify monomials and polynomials and determine their degree in this interactive tutorial.

This is part 1 in a two-part series. **Click HERE to open Part 2**.

Learn how to add and subtract polynomials in this online tutorial. You will learn how to combine like terms and then use the distribute property to subtract polynomials.

This is part 2 of a two-part lesson. Click below to open part 1.

## Student Resources

## Original Student Tutorials

Learn how to add and subtract polynomials in this online tutorial. You will learn how to combine like terms and then use the distribute property to subtract polynomials.

This is part 2 of a two-part lesson. Click below to open part 1.

Type: Original Student Tutorial

Learn how to identify monomials and polynomials and determine their degree in this interactive tutorial.

This is part 1 in a two-part series. **Click HERE to open Part 2**.

Type: Original Student Tutorial

## Student Center Activity

This video will demonstrate how to multiply polynomials.

Type: Student Center Activity

## Tutorials

This video tutorial shows students: the standard form of a polynomial, how to identify polynomials, how to determine the degree of a polynomial, how to add and subtract polynomials, and how to represent the area of a shape as an addition or subtraction of polynomials.

Type: Tutorial

This video explains how to subtract polynomials with multiple variables and reinforces how to distribute a negative number.

Type: Tutorial

This video covers squaring a binomial with two variables. Students will be given the area of a square.

Type: Tutorial

The video tutorial discusses about two typical polynomial multiplications. First, squaring a binomial and second, product of a sum and difference.

Type: Tutorial

This tutorial will help the learners practice multiplication of polynomials. Learners will understand that when they multiply expressions with more than two terms, they need to make sure each term in the first expression multiplies every term in the second expression.

Type: Tutorial

Binomials are the polynomials with two terms. This tutorial will help the students learn about the multiplication of binomials. In multiplication, we need to make sure that each term in the first set of parenthesis multiplies each term in the second set.

Type: Tutorial

## Virtual Manipulatives

This resource will assess students' understanding of addition and subtraction of polynomials.

Type: Virtual Manipulative

This virtual manipulative is intended to allow the student to practice multiplication of binomials. The student should understand how to use algebra tiles before using this tool.

Type: Virtual Manipulative

## Parent Resources

## Tutorials

This video tutorial shows students: the standard form of a polynomial, how to identify polynomials, how to determine the degree of a polynomial, how to add and subtract polynomials, and how to represent the area of a shape as an addition or subtraction of polynomials.

Type: Tutorial

The video tutorial discusses about two typical polynomial multiplications. First, squaring a binomial and second, product of a sum and difference.

Type: Tutorial

This tutorial will help the learners practice multiplication of polynomials. Learners will understand that when they multiply expressions with more than two terms, they need to make sure each term in the first expression multiplies every term in the second expression.

Type: Tutorial

Binomials are the polynomials with two terms. This tutorial will help the students learn about the multiplication of binomials. In multiplication, we need to make sure that each term in the first set of parenthesis multiplies each term in the second set.

Type: Tutorial

This resource is a step-by-step tutorial on how to multiply polynomials.

Type: Tutorial

## Virtual Manipulatives

This resource will assess students' understanding of addition and subtraction of polynomials.

Type: Virtual Manipulative

This virtual manipulative is intended to allow the student to practice multiplication of binomials. The student should understand how to use algebra tiles before using this tool.

Type: Virtual Manipulative